Good questions.. Very good questions.
It definitely won't move to the other top 20 coins though. I'll explain why before answering the first question.
What you have to understand about bitcoin is where the intrinsic value of it comes from.
It comes from the technology its self. It's not necessarily that "everyone chooses to use it". That's a requirement, yes, but it's not where the intrinsic value lies. It's more of a consequence OF that instrinsic value.
The intrinsic value comes from :-
1) It's got a hard limit. This has been something that's been really hard to do with assets traditionally. It's why gold has been a popular choice. Many socieities in human history used a variety of things as a store of value which at the time were limited.
One example was the Yap islands who manufactured huge stones called Rai stones.
Their idea, and it was light years ahead of its time was that energy and money are interchangeable. Money is after all and exchange of energy isn't it? All money and all assets are energy. It's just conversion of energy.
If I have a farm and I grow potatoes then I had to put my own energy into the farm. I'm essentially converting biomechanical energy into another form of energy in the form of a potato.
Now, the other key thing is the *thing*, and by *thing* I am referring to any type of asset, money, food or object. The thing needs to have some value for other people. If a thing doesn't have value, you are wasting energy.
If potatoes were completely useless, I am converting biomechanical energy into potatoes, but the potatoes have no value. Imagine they're not edible and have no other use. So I have just wasted my energy. If I continue through life wasting energy, I will die. I am outputing more energy than I can get back in. I need energy to re-fuel my biomechanics. At the simplest level I can hunt. I convert what biomechanical energy I have available, into an even more abundant form of energy. Meat I can consume. I consume 10 points of energy, and I can 50 points of energy. If for example, 1 meal from a hunt will fuel me to hunt 5 more animals.
Now, fortunately my potatoes that I've grown have value to you.
You don't know how to grow potatoes, and you're fucking HUNGRY.
However, you are a woodworker and can craft furniture. You convert your biomechanical energy into another type of energy which is a chair. That chair is ENERGY. The amount of energy it is depends on how useful it is.
All monetary energy has energy based on how useful it is to other people, or more broadly other beings that can convert energy in a system. (If you want to expand this more universally, and even in the animal kingdom there is energy exchanges through natural systems)
My potatoes are monetary energy.
Your chair is monetary energy.
The exact value? That's determined through our individual exchange.
I give you 25 potatoes per week for the next 4 weeks, and you give me a chair.
You consume those potatoes, converting the energy into biomechanical energy.
I use my chair to chair to rest, to work, to do whatever I need to do with a chair. It enhances my life giving me some net energy positive.
For those that have a lot of excess energy, they may swap energy for visual things like pretty objects which can be made from gold. This is why gold has always been valuable/useful. People like pretty things. It makes them feel good looking at it.
Back to the Yap islands... Now we hopefully understand how all money/assets are energy.
They realized this..
Now, one of the other problems we have is when we're trading random objects it's very hard to build up and store wealth. We need an easy way that we all agree upon will be used as an exchange of wealth, so instead of you giving me a chair, I can accept some object, which I can then store and trade later.
Because I might not necessarily need a chair today, and I might not need something YOU have, but you might need my potatoes, Jim in a nearby village needs your chairs, and I need Jim's labor to help with me my farm. It becomes then very hard to trade and convert the monetary energy doesn't it?
So this is why we need some "token", or some "object".
Now, if money is energy, then this object needs to be related to energy.
Creating US dollars requires almost no energy. You can print print print. It only works through a central organization(the fed) controlling the money supply. This is not good.
What the leaders in the Yap islands did was they came up with this idea to use "Rai stones" as money. These Rai stones were HUGE and took a long time to make. Thus solving the problem of flooding the market. It took years to build them and they maintained ownership through an oral history. Which, if you think about it is kind of like bitcoin.. To change ownership of a Rai stone, it probably wasn't enough for 1 chieftan to say it's changed, they would have needed consensus. They would have had their own rudimentary form of estalblishing consensus, which is at the heart of all crypto.
Things went wrong when Europeans with more advanced tools created them and tried to trade using them. The market was essentially flooded and they became devalued.
Now, back to point 1.
Bitcoin having the hard limit of 21 million means no one can ever flood the market with bitcoins.
This solves the 1st requirement we need for a token or object to represent money, value, or ENERGY.
2) It should be decentralized
This is important so no one can control anyone else. If it's not decentralized you are at the mercy of another party, like the Fed, the banks, the system and the governments.
3) It should be secure
You don't want something that's not secure. The Rai stones were too heavy to just steal, so they satisfied this requirement.
The more secure the better, and bitcoin is INCREDIBLY secure and has over a decade of history proving this.
4) It should be easy to transfer ownership.
If you can't change ownership easily, you can't trade. Bitcoin makes it easier than any other object in the world to transfer ownership. We could trade bitcoin with any amount we like in the space of 30 minutes with the 2 of us being anywhere in the world.
These are, at least what I can think of just now the key requirements for a store of wealth, money, assets or ENERGY as it ultimately is.
Ie, bitcoin is digital energy.
Potatoes are food energy.
A chair is a furniture energy.
Digital energy is more useful than food energy, because food energy doesn't last, and furniture energy is clumsy, not limited and not easily transferrable globally..
Once all these things are satisfied, and the more that people realize they're all satisfied, the thing can then become widely adopted.
Not all cryptos satisfy this requirement, and not all are meant to.
Doge for example has an infinite amount to be mined. It's not meant to be a long term store of value. Ie, a long term store of energy. 5 billion doge per year can be mined.
Doge is more useful for converting bitcoin digital energy to doge digital energy and trading it. This is a good thing, and it keeps people trading in doge. It's better to do active trade in a currency that inflates because it keeps the pool of available tokens in the market high and people trading and not hoarding.
Doge is meant to encourage energy movement.
Bitcoin is meant to encourage energy storage for later use.
Now, bitcoin is the one that the world chose.
In 2140 once the last bitcoin has been mined, people won't stop using it as a store of value. It still has the same use.
Your first question you asked won't the value stop going up when there's no more to be mined.. You've got that backwards.
The less there is available, the higher the price goes. Think about it, what's happening with bitcoin now? Every 4 years the mining rewards are cut in half, and this causes supply to decrease and price to go up.
It's not the other way around. If you flood the market with bitcoins, the price crashes.
So all that happens after the last bitcoin is mined, is the supply is even more limited, and the price will continue to rise as demand for it increases. Rising prices cause demand to increase more as people continue to trust that it's a store of value/energy.
If I farm for decades, I want a way to capture all that energy and store it for my future, or for my family after me. Until bitcoin it's hard for me to capture that energy for future generations. Now, with bitcoin, everyone can capture their energy and store it safely.
The world isn't going to suddenly sell all their bitcoin and buy another crypto that's both less in demand, more volatile and has inflationary properties.

That would be utter madness.
The world will keep pumping their energy into bitcoin, and THIS is why the price of bitcoin will keep going up forever. It's the accumulated energy of mankind.